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<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.linear_model</span></code>.lars_path</a><ul>
<li><a class="reference internal" href="#examples-using-sklearn-linear-model-lars-path">Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.linear_model.lars_path</span></code></a></li>
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  <div class="section" id="sklearn-linear-model-lars-path">
<h1><a class="reference internal" href="../classes.html#module-sklearn.linear_model" title="sklearn.linear_model"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.linear_model</span></code></a>.lars_path<a class="headerlink" href="#sklearn-linear-model-lars-path" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="sklearn.linear_model.lars_path">
<code class="sig-prename descclassname">sklearn.linear_model.</code><code class="sig-name descname">lars_path</code><span class="sig-paren">(</span><em class="sig-param">X</em>, <em class="sig-param">y</em>, <em class="sig-param">Xy=None</em>, <em class="sig-param">Gram=None</em>, <em class="sig-param">max_iter=500</em>, <em class="sig-param">alpha_min=0</em>, <em class="sig-param">method='lar'</em>, <em class="sig-param">copy_X=True</em>, <em class="sig-param">eps=2.220446049250313e-16</em>, <em class="sig-param">copy_Gram=True</em>, <em class="sig-param">verbose=0</em>, <em class="sig-param">return_path=True</em>, <em class="sig-param">return_n_iter=False</em>, <em class="sig-param">positive=False</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/linear_model/_least_angle.py#L29"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.linear_model.lars_path" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute Least Angle Regression or Lasso path using LARS algorithm [1]</p>
<p>The optimization objective for the case method=’lasso’ is:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">n_samples</span><span class="p">))</span> <span class="o">*</span> <span class="o">||</span><span class="n">y</span> <span class="o">-</span> <span class="n">Xw</span><span class="o">||^</span><span class="mi">2_2</span> <span class="o">+</span> <span class="n">alpha</span> <span class="o">*</span> <span class="o">||</span><span class="n">w</span><span class="o">||</span><span class="n">_1</span>
</pre></div>
</div>
<p>in the case of method=’lars’, the objective function is only known in
the form of an implicit equation (see discussion in [1])</p>
<p>Read more in the <a class="reference internal" href="../linear_model.html#least-angle-regression"><span class="std std-ref">User Guide</span></a>.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl>
<dt><strong>X</strong><span class="classifier">None or array-like of shape (n_samples, n_features)</span></dt><dd><p>Input data. Note that if X is None then the Gram matrix must be
specified, i.e., cannot be None or False.</p>
<div class="deprecated">
<p><span class="versionmodified deprecated">Deprecated since version 0.21: </span>The use of <code class="docutils literal notranslate"><span class="pre">X</span></code> is <code class="docutils literal notranslate"><span class="pre">None</span></code> in combination with <code class="docutils literal notranslate"><span class="pre">Gram</span></code> is not
<code class="docutils literal notranslate"><span class="pre">None</span></code> will be removed in v0.23. Use <a class="reference internal" href="sklearn.linear_model.lars_path_gram.html#sklearn.linear_model.lars_path_gram" title="sklearn.linear_model.lars_path_gram"><code class="xref py py-func docutils literal notranslate"><span class="pre">lars_path_gram</span></code></a>
instead.</p>
</div>
</dd>
<dt><strong>y</strong><span class="classifier">None or array-like of shape (n_samples,)</span></dt><dd><p>Input targets.</p>
</dd>
<dt><strong>Xy</strong><span class="classifier">array-like of shape (n_samples,) or (n_samples, n_targets),             default=None</span></dt><dd><p>Xy = np.dot(X.T, y) that can be precomputed. It is useful
only when the Gram matrix is precomputed.</p>
</dd>
<dt><strong>Gram</strong><span class="classifier">None, ‘auto’, array-like of shape (n_features, n_features),             default=None</span></dt><dd><p>Precomputed Gram matrix (X’ * X), if <code class="docutils literal notranslate"><span class="pre">'auto'</span></code>, the Gram
matrix is precomputed from the given X, if there are more samples
than features.</p>
<div class="deprecated">
<p><span class="versionmodified deprecated">Deprecated since version 0.21: </span>The use of <code class="docutils literal notranslate"><span class="pre">X</span></code> is <code class="docutils literal notranslate"><span class="pre">None</span></code> in combination with <code class="docutils literal notranslate"><span class="pre">Gram</span></code> is not
None will be removed in v0.23. Use <a class="reference internal" href="sklearn.linear_model.lars_path_gram.html#sklearn.linear_model.lars_path_gram" title="sklearn.linear_model.lars_path_gram"><code class="xref py py-func docutils literal notranslate"><span class="pre">lars_path_gram</span></code></a> instead.</p>
</div>
</dd>
<dt><strong>max_iter</strong><span class="classifier">int, default=500</span></dt><dd><p>Maximum number of iterations to perform, set to infinity for no limit.</p>
</dd>
<dt><strong>alpha_min</strong><span class="classifier">float, default=0</span></dt><dd><p>Minimum correlation along the path. It corresponds to the
regularization parameter alpha parameter in the Lasso.</p>
</dd>
<dt><strong>method</strong><span class="classifier">{‘lar’, ‘lasso’}, default=’lar’</span></dt><dd><p>Specifies the returned model. Select <code class="docutils literal notranslate"><span class="pre">'lar'</span></code> for Least Angle
Regression, <code class="docutils literal notranslate"><span class="pre">'lasso'</span></code> for the Lasso.</p>
</dd>
<dt><strong>copy_X</strong><span class="classifier">bool, default=True</span></dt><dd><p>If <code class="docutils literal notranslate"><span class="pre">False</span></code>, <code class="docutils literal notranslate"><span class="pre">X</span></code> is overwritten.</p>
</dd>
<dt><strong>eps</strong><span class="classifier">float, optional</span></dt><dd><p>The machine-precision regularization in the computation of the
Cholesky diagonal factors. Increase this for very ill-conditioned
systems. By default, <code class="docutils literal notranslate"><span class="pre">np.finfo(np.float).eps</span></code> is used.</p>
</dd>
<dt><strong>copy_Gram</strong><span class="classifier">bool, default=True</span></dt><dd><p>If <code class="docutils literal notranslate"><span class="pre">False</span></code>, <code class="docutils literal notranslate"><span class="pre">Gram</span></code> is overwritten.</p>
</dd>
<dt><strong>verbose</strong><span class="classifier">int, default=0</span></dt><dd><p>Controls output verbosity.</p>
</dd>
<dt><strong>return_path</strong><span class="classifier">bool, default=True</span></dt><dd><p>If <code class="docutils literal notranslate"><span class="pre">return_path==True</span></code> returns the entire path, else returns only the
last point of the path.</p>
</dd>
<dt><strong>return_n_iter</strong><span class="classifier">bool, default=False</span></dt><dd><p>Whether to return the number of iterations.</p>
</dd>
<dt><strong>positive</strong><span class="classifier">bool, default=False</span></dt><dd><p>Restrict coefficients to be &gt;= 0.
This option is only allowed with method ‘lasso’. Note that the model
coefficients will not converge to the ordinary-least-squares solution
for small values of alpha. Only coefficients up to the smallest alpha
value (<code class="docutils literal notranslate"><span class="pre">alphas_[alphas_</span> <span class="pre">&gt;</span> <span class="pre">0.].min()</span></code> when fit_path=True) reached by
the stepwise Lars-Lasso algorithm are typically in congruence with the
solution of the coordinate descent lasso_path function.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>alphas</strong><span class="classifier">array-like of shape (n_alphas + 1,)</span></dt><dd><p>Maximum of covariances (in absolute value) at each iteration.
<code class="docutils literal notranslate"><span class="pre">n_alphas</span></code> is either <code class="docutils literal notranslate"><span class="pre">max_iter</span></code>, <code class="docutils literal notranslate"><span class="pre">n_features</span></code> or the
number of nodes in the path with <code class="docutils literal notranslate"><span class="pre">alpha</span> <span class="pre">&gt;=</span> <span class="pre">alpha_min</span></code>, whichever
is smaller.</p>
</dd>
<dt><strong>active</strong><span class="classifier">array-like of shape (n_alphas,)</span></dt><dd><p>Indices of active variables at the end of the path.</p>
</dd>
<dt><strong>coefs</strong><span class="classifier">array-like of shape (n_features, n_alphas + 1)</span></dt><dd><p>Coefficients along the path</p>
</dd>
<dt><strong>n_iter</strong><span class="classifier">int</span></dt><dd><p>Number of iterations run. Returned only if return_n_iter is set
to True.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="sklearn.linear_model.lars_path_gram.html#sklearn.linear_model.lars_path_gram" title="sklearn.linear_model.lars_path_gram"><code class="xref py py-obj docutils literal notranslate"><span class="pre">lars_path_gram</span></code></a></dt><dd></dd>
<dt><a class="reference internal" href="sklearn.linear_model.lasso_path.html#sklearn.linear_model.lasso_path" title="sklearn.linear_model.lasso_path"><code class="xref py py-obj docutils literal notranslate"><span class="pre">lasso_path</span></code></a></dt><dd></dd>
<dt><code class="xref py py-obj docutils literal notranslate"><span class="pre">lasso_path_gram</span></code></dt><dd></dd>
<dt><a class="reference internal" href="sklearn.linear_model.LassoLars.html#sklearn.linear_model.LassoLars" title="sklearn.linear_model.LassoLars"><code class="xref py py-obj docutils literal notranslate"><span class="pre">LassoLars</span></code></a></dt><dd></dd>
<dt><a class="reference internal" href="sklearn.linear_model.Lars.html#sklearn.linear_model.Lars" title="sklearn.linear_model.Lars"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Lars</span></code></a></dt><dd></dd>
<dt><a class="reference internal" href="sklearn.linear_model.LassoLarsCV.html#sklearn.linear_model.LassoLarsCV" title="sklearn.linear_model.LassoLarsCV"><code class="xref py py-obj docutils literal notranslate"><span class="pre">LassoLarsCV</span></code></a></dt><dd></dd>
<dt><a class="reference internal" href="sklearn.linear_model.LarsCV.html#sklearn.linear_model.LarsCV" title="sklearn.linear_model.LarsCV"><code class="xref py py-obj docutils literal notranslate"><span class="pre">LarsCV</span></code></a></dt><dd></dd>
<dt><a class="reference internal" href="sklearn.decomposition.sparse_encode.html#sklearn.decomposition.sparse_encode" title="sklearn.decomposition.sparse_encode"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sklearn.decomposition.sparse_encode</span></code></a></dt><dd></dd>
</dl>
</div>
<p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="r2391cff0bbde-1"><span class="brackets">1</span></dt>
<dd><p>“Least Angle Regression”, Efron et al.
<a class="reference external" href="http://statweb.stanford.edu/~tibs/ftp/lars.pdf">http://statweb.stanford.edu/~tibs/ftp/lars.pdf</a></p>
</dd>
<dt class="label" id="r2391cff0bbde-2"><span class="brackets">2</span></dt>
<dd><p><a class="reference external" href="https://en.wikipedia.org/wiki/Least-angle_regression">Wikipedia entry on the Least-angle regression</a></p>
</dd>
<dt class="label" id="r2391cff0bbde-3"><span class="brackets">3</span></dt>
<dd><p><a class="reference external" href="https://en.wikipedia.org/wiki/Lasso_(statistics)">Wikipedia entry on the Lasso</a></p>
</dd>
</dl>
</dd></dl>

<div class="section" id="examples-using-sklearn-linear-model-lars-path">
<h2>Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.linear_model.lars_path</span></code><a class="headerlink" href="#examples-using-sklearn-linear-model-lars-path" title="Permalink to this headline">¶</a></h2>
<div class="sphx-glr-thumbcontainer" tooltip="Computes Lasso Path along the regularization parameter using the LARS algorithm on the diabetes..."><div class="figure align-default" id="id4">
<img alt="../../_images/sphx_glr_plot_lasso_lars_thumb.png" src="../../_images/sphx_glr_plot_lasso_lars_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/linear_model/plot_lasso_lars.html#sphx-glr-auto-examples-linear-model-plot-lasso-lars-py"><span class="std std-ref">Lasso path using LARS</span></a></span><a class="headerlink" href="#id4" title="Permalink to this image">¶</a></p>
</div>
</div><div class="clearer"></div></div>
</div>


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